Question

10.

a) Real GDP per capita in Brainland in 2020 is $20,000. Due to past investment in its education system and infrastructure, Brainland has been experiencing a growth rate in real GDP per capita of 7% per year. Assume real GDP per capita continues to grow at 7% for the next 30 years. Use the rule of 70 to determine what real GDP per capita would be in the year 2050.

   b) Real GDP per capita in the neighboring country of Swampland is also $20,000 in 2020. However in Swampland infrastructure is crumbling, the education system is in decline, there is civil unrest and the government is characterized by mismanagement and corruption. The growth rate in real GDP per capita has declined to .5% per year and is expected to remain at .5% for the next 30 years. Use the compounding growth formula to determine what real GDP per capita would be in Swampland in the year 2050.

Answer 1

a) Real GDP per capita in Brainland is $20,000

Growth rate of real GDP per capita = 7%

Rule of 70 says that it take (70 / Growth rate per year) = (70 / 7) = 10 years to double real GDP per capita

In 10 years, real GDP per capita in Brainland doubles. In 10 next 10 years, real GDP again doubles and finally in next 10 years, it again gets doubled.

In total 30 years, real GDP per capita is 20,000 * 2 * 2 * 2 = 160,000

b) Real GDP is swampland in 2020 is $20,000

Growth rate of real GDP per capita = 0.5%

In next 30 years, real GDP of swampland would be: 20,000 * (1 + 0.005)^³⁰ = 23,228